I would recommend TR6223 which leaves Leicester at 19:09 and arrives in Cambridge by 20:54.
Please book that one for 7 people.
train-day train-departure train-destination train-leaveat train-people
train-day train-departure train-destination train-leaveat train-people
train-day train-departure train-destination train-leaveat train-people
train-day train-departure train-destination train-leaveat train-people